Lindblad, Hans; Soffer, Avy Scattering and small data completeness for the critical nonlinear Schrödinger equation. (English) Zbl 1106.35099 Nonlinearity 19, No. 2, 345-353 (2006). The authors consider the problem of scattering for the critical nonlinear Schrödinger equation (NLS) in one space dimension. They prove asymptotic completeness of the NLS with long range nonlinearities. The authors obtain an explicit construction of the phase function and the asymptotic form of the solution as well. They also prove the existence of wave operators for large data in the repulsive case and small data in the general nonlinear case. Reviewer: A. D. Osborne (Keele) Cited in 27 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35P25 Scattering theory for PDEs Keywords:scattering; phase function; existence of wave operators PDFBibTeX XMLCite \textit{H. Lindblad} and \textit{A. Soffer}, Nonlinearity 19, No. 2, 345--353 (2006; Zbl 1106.35099) Full Text: DOI arXiv